Go-or-grow-or-die as a framework for the mathematical modeling of glioblastoma dynamics

Abstract

We investigate a three-dimensional reaction–diffusion model of avascular glioblastoma growth, introducing a new go-or-grow-or-die framework that incorporates reversible phenotypic switching between migratory and proliferative states, while accounting for the contribution of necrotic cells. To model necrotic cell accumulation, a quasi-steady-state approximation is employed, allowing the necrotic population to be expressed as a function of proliferating cell density. Analytical and numerical analyses of the model reveal that the traveling wave speed is consistently lower than that predicted by the classical Fisher–Kolmogorov–Petrovsky–Piskunov equation, highlighting the significance of phenotypic heterogeneity. In particular, we confirm the role of the switching parameter in modulating invasion speed. Approximate wave profiles derived using Canosa’s method show strong agreement with numerical simulations. Furthermore, model predictions are validated against experimental data for the $U87WT$ glioblastoma cell line, demonstrating improved accuracy in capturing tumor invasion when both phenotypic switching and necrosis are included. These findings underscore the importance of the go-or-grow-or-die framework in understanding tumor progression and establish a novel, generalizable framework for modeling cancer dynamics.